Single View Seafloor Recovery from Imaging Sonar via Differentiable Rendering

Sonar is often the only modality suitable for high-resolution imaging underwater due to light attenuation and turbidity. Forward-looking imaging sonar provides measurements over range and horizontal angle but collapses vertical structure into a flat image, creating ambiguities that make 3D recovery challenging. A common use case for imaging sonar is underwater terrain mapping (bathymetry), yet current methods require many views, expensive multi-sensor setups, or significant training data, which limits use and adaptability to new environments. We present a training-free method that recovers bathymetry from a single sonar image in under 30 seconds via differentiable rendering, conditioned on a known seafloor tilt. To our knowledge, this is the first differentiable rendering approach for single-view height recovery in sonar. Our method implements differentiable sonar ray tracing and optimizes an explicit height field to reproduce the target image. On synthetic datasets, our approach outperforms a supervised CNN under distribution shift and remains close on rough terrain, while the CNN wins in-distribution. By modeling physically grounded priors of the sonar process, our method adapts across sensor configurations and environments without training data.

Kuramoto Orientation Diffusion Models

Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role of phase synchronization in biological systems, we propose a score-based generative model built on periodic domains by leveraging stochastic Kuramoto dynamics in the diffusion process. In neural and physical systems, Kuramoto models capture synchronization phenomena across coupled oscillators -- a behavior that we re-purpose here as an inductive bias for structured image generation. In our framework, the forward process performs \textit{synchronization} among phase variables through globally or locally coupled oscillator interactions and attraction to a global reference phase, gradually collapsing the data into a low-entropy von Mises distribution. The reverse process then performs \textit{desynchronization}, generating diverse patterns by reversing the dynamics with a learned score function. This approach enables structured destruction during forward diffusion and a hierarchical generation process that progressively refines global coherence into fine-scale details. We implement wrapped Gaussian transition kernels and periodicity-aware networks to account for the circular geometry. Our method achieves competitive results on general image benchmarks and significantly improves generation quality on orientation-dense datasets like fingerprints and textures. Ultimately, this work demonstrates the promise of biologically inspired synchronization dynamics as structured priors in generative modeling.